Grimbergen is my home base, and my office overlooks Brussels airport.
Brussels ATC are fine - but remember you will be flying VFR in Class B/C. I think though, you will find the fees quite high, and I suspect you need a handling agent, there (check this though). Its not really intended for light GA, but its not impossible. The former SABENA flying club used to fly their a/c the 5 miles from Grimbergen to Brussels for maintenenace, as a matter of routine.
Remember, if coming from the UK you are not part of Shengan. This means that you MUST depart from, and land at, a customs airport. Antwerp (North) and Charleroi (South) both fulfill that role - but Grimbergen (nearest) doesn't - so you will have to stop off on the way at any customs airfield e.g. Calais, Ostende before landing at Grimbergen.
Grimbergen is a PPR airfield, mainly used by the flying clubs, resident a/c and some GA visitors - but it is not configured as a GA substitute for Brussels. It is very close to Brussels and has a shortened circuit with an early base turn for landing on 01, to remain clear of Brussels airport. A little care is all that's required, though.
Transport from Grimbergen to the city is available, but don't count on it being quick. Taxis are not cheap here, either.
If you need more - let me know.
GB